(1) Mathematical Institute, Tohoku University, Sendai, 980-8578, Japan;(2) Department of Mathematics, Faculty of Science, Kyoto University, Kyoto, 606-8502, Japan
Abstract:
We prove the harmonicity of totally geodesic maps from a Riemannian manifold to a nonpositively curved metric space in the sense of Alexandrov for both Korevaar-Schoen-type and Cheeger-type energies. This enables us to make many examples of harmonic maps of an unknown type. We also construct an example of totally geodesic map between CAT(0)-spaces which is not harmonic.Mathematics Subject Classification (2000): 53C22, 53C43, 58E20